The determinant left| {,begin{array}{*{20}{c} | vedclass

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Question

(d) $\left| {\,\begin{array}{*{20}{c}}{4 + {x^2}}&{ - 6}&{ - 2}\{ - 6}&{9 + {x^2}}&3\{ - 2}&3&{1 + {x^2}}\end{array}} ight

Vedclass · Accepted Answer

${x^5}$

Vedclass · Answer

(d) $\left| {\,\begin{array}{*{20}{c}}{4 + {x^2}}&{ - 6}&{ - 2}\{ - 6}&{9 + {x^2}}&3\{ - 2}&3&{1 + {x^2}}\end{array}} ight| = {x^4}(14 + {x^2})$ $ = x.{x^3}(14 + {x^2})$

Hence, the determinant is divisible by $x$,${x^3}$ and $(14 + {x^2})$,

but not divisible by ${x^5}$.

The determinant $\left| {\,\begin{array}{*{20}{c}}{4 + {x^2}}&{ - 6}&{ - 2}\\{ - 6}&{9 + {x^2}}&3\\{ - 2}&3&{1 + {x^2}}\end{array}\,} \right|$ is not divisible by

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